Varying Constants and the Brans-Dicke theory: a new landscape in cosmological energy conservation

Abstract

We develop the Brans-Dicke theory of gravity in the context of varying constants of Nature. Using the unimodular formalism of General Relativity, we create a platform to provide physical relational times giving the evolution of physical constants. We therefore review the ideas and experiments behind varying constants, mostly focusing on the speed of light and the gravitational constant. Then, we apply this idea to the energy conservation in cosmology, illustrating the arising patterns. Motivated by a varying gravitational constant resulting from Mach's principle, we develop the unimodular formalism of varying constants in the Brans-Dicke theory. Doing so, we obtain several original results, some of which can be compared with phenomenological observation. Finally, we suggest how a varying Brans-Dicke parameter could be linked to the Cosmological Constant problem.